BAGHDAD, Iraq (CNN) -- The U.S. military said Tuesday it has seized a letter from Iraqi insurgents believed to be intended for Jordanian-born militant Abu Musab al-Zarqawi complaining about low morale among followers and weakening support for the insurgency.

The authenticity of the letter -- which the military said American troops found Thursday in a raid in Baghdad -- could not be independently verified.

The letter -- which never refers to al-Zarqawi by name -- is written to Sheik Abu Ahmad, a name not known to be used by the militant leader or his followers. But supporters often call al-Zarqawi the Sheik or Sheik Abu Musab in letters and on Web sites.

"What has happened to myself and my brothers is an unforgivable crime, but God will punish the oppressor," the letter reads. "I swear by God that you will be asked about what happened to us because you have not asked about the situation of the migrants. Morale is down and there is fatigue among mujahedeen ranks.

"There is discrimination by some of the brethren emirs. God would not accept such actions, and a simple mistake delays victory, so what about big mistakes and gross guilts? Many underestimate them and are lenient toward them."

The letter is dated April 27, the military said.

The author of the letter also "admonishes 'the Sheik' for abandoning his followers" after last year's U.S. siege on Falluja, west of Baghdad.

U.S. forces led an assault then on the Sunni Triangle city's terrorist network believed to be run by al-Zarqawi.

Because of the "continuous pressure by Iraqi and [U.S.-led] coalition forces," a military statement said, al-Zarqawi has relied on his cell leaders to conduct operations while he is forced to evade being killed or captured.

Pentagon officials said last week that U.S. troops nearly caught al-Zarqawi in February after receiving a tip that he might be traveling to Ramadi, west of Falluja. (Full story)

The author of the letter, the military said, is a member of the terrorist group known as al Qaeda in Iraq.

The author's name is Abu Asim al-Qusaymi al-Yemeni, the military statement said.

Pentagon spokesman Bryan Whitman said the letter reflects "a certain amount of proof that [al-Zarqawi's] influence and effectiveness is deteriorating."

Key posts under discussion

Iraqi politicians are putting the finishing touches on the nation's new government Tuesday. Shiite Arab leader Ibrahim al-Jaafari was sworn in as prime minister as Iraq's first democratically elected government after Saddam Hussein's regime.

"On this historic day I would like to pay tribute to the Iraqi people because of this historic accomplishment," President Jalal Talabani said. Referring to the new officials, he said, "I think they are capable of this mission."

On Thursday, al-Jaafari announced 36 Cabinet positions in the new government -- some of them temporary. New Cabinet members were sworn in one by one Tuesday -- altogether 28.

The full Iraqi government will not be in place Tuesday because key ministry posts remain under discussion. Among those ministries are oil, defense, electricity, human rights, and industry and minerals, which are in temporary hands, and two deputy prime ministries, which are unfilled. (Cabinet list)

It is unclear why two Sunni Arabs who had been chosen for the ministers of women affairs and provinces affairs were not sworn in. But two other Sunnis -- the trade and culture ministers -- were installed.

Sunnis -- who dominated under Saddam -- did not turn out in significant numbers for the January 30 elections. But Iraqi politicians have been making efforts to bring them into the new government.

U.S. pilot's body found

The U.S. military early Tuesday found the body of a pilot from one of two missing Marine Corps F/A-18 jets that Navy officials believe collided while flying in operations in Iraq.

"The status of the second crew member is unknown at this time, and search efforts continue," a military statement said.

The crew of the aircraft carrier USS Carl Vinson lost contact with the planes about 10:10 p.m. Monday (2:10 p.m. ET), the military said. The statement said there was no indication of hostile fire in the area at the time.

Navy officials said they think the jets collided in bad weather during the routine mission.

Late last year, Marine Corps officials said a sharp increase in deadly accidents involving Marine aircraft had forced a close look at possible causes of the mishaps. (Full story)

Other developments

Two Bulgarian soldiers were killed Tuesday in a traffic accident in southern Iraq, said a statement from the U.S.-led multinational forces. A Hummer with the soldiers overturned near Basra, the statement said. Ten Bulgarians have died in the Iraq war.

A bomb detonated Tuesday near an Iraqi police convoy in Baghdad, wounding three people, a police official said. The bomb was planted in a pickup in the Ghaziyilia area. A police officer and two civilians were wounded.

Coalition forces battled suspected insurgents Monday night in western Iraq, killing at least 12 in a firefight and following airstrike, a U.S. military statement said. Six coalition forces were wounded. "Coalition forces found fake identification cards, foreign currency and other evidence that provided proof of direct ties with the [al-Zarqawi] terrorist network as well as with networks outside of Iraq," the statement said.

Disputing the conclusions of a U.S. report into the death of an Italian intelligence agent, an Italian investigation released Monday found that stress and inexperience among American soldiers played a role in the shooting. A classified version of the U.S. report painted a grim picture of insurgency in Baghdad in the months leading up to the March shooting, including some details not made public elsewhere. (Full story)

U.S. Army Pfc. Lynndie England -- the reservist whose image symbolized the Abu Ghraib prison scandal in Iraq -- pleaded guilty Monday to charges related to the abuse at the Baghdad facility. The sentencing phase for England began Tuesday. (Full story)